Security and the incalculable

Abstract In this article, I explore a specific relation between mathematics and security calculations. Recalling the confrontations between the mathematician Alan Turing and the philosopher Ludwig Wittgenstein in the 1930s, I am interested in the relationship between intuition and ingenuity. During Wittgenstein’s 1930 lectures on the foundations of mathematics, Turing interjects in order to insist upon the capacity of number: ‘one can make predictions’. Wittgenstein replies that mathematics ‘makes no predictions’, but instead is a form of grammar: ‘taken by itself we shouldn’t know what to do with it; it’s useless. But there is all kind of use for it as part of a calculus’. It is just such a formulation of a calculus or grammar – ‘decision trees’, ‘event trees’, ‘attribute-based algorithms’ – that characterizes contemporary security. As for Turing, the logic comprises ‘two faculties, which we may call intuition and ingenuity’. The intuitive realm of imagination and speculation reaches toward a possible solution, while the ingenuity seeks arrangements of propositions. The advent of ‘rules-based’ and ‘risk-based’ security decisions, then, are always already political because they precisely involve combinatorial possibilities whose arrangement has effects in the world.